THE CAUCHY INTEGRAL OF MANY COMPLEX VARIABLES PASSIVE OPERATORS AND MULTIDIMENSIONAL DISPERSION RELATIONS

This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance

Strong Earthquakes in the Yunnan-Sichuan Region: Evaluation of a Forward Long-to-intermediate-term PI Forecast

Since the initial international cooperation in the framework of Collaboratory for the Study of Earthquake Predictability(CSEP)in 2007,a lot of forecast models have been developed and served for the earthquake forecasting experiment in different CSEP testing centers(Schorlemmer et al.,2018).

Landslide initiation and runout susceptibility modeling in the context of hill cutting and rapid urbanization: a combined approach of weights of evidence and spatial multicriteria

Rainfall induced landslides are a common threat to the communities living on dangerous hillslopes in Chittagong Metropolitan Area, Bangladesh. Extreme population pressure, indiscriminate hill cutting, increased precipitation events due to global warming and associated unplanned urbanization in the hills are exaggerating landslide events. The aim of this article is to prepare a scientifically accurate landslide susceptibility map by combining landslide initiation and runout maps. Land cover, slope, soil permeability, surface geology, precipitation, aspect, and distance to hill cut, road cut, drainage and stream network factor maps were selected by conditional independence test. The locations of 56 landslides were collected by field surveying. A weight of evidence(Wo E) method was applied to calculate the positive(presence of landslides) and negative(absence of landslides) factor weights. A combination of analytical hierarchical process(AHP) and fuzzymembership standardization(weighs from 0 to 1) was applied for performing a spatial multi-criteria evaluation. Expert opinion guided the decision rule for AHP. The Flow-R tool that allows modeling landslide runout from the initiation sources was applied. The flow direction was calculated using the modified Holmgren's algorithm. The AHP landslide initiation and runout susceptibility maps were used to prepare a combined landslide susceptibility map. The relative operating characteristic curve was used for model validation purpose. The accuracy of Wo E, AHP, and combined susceptibility map was calculated 96%, 97%, and 98%, respectively.

HARDY-LITTLEWOOD-POLYA INEQUALITY FOR A LINEAR DIFFERENTIAL OPERATOR AND SOME RELATED OPTIMAL PROBLEMS

In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.

Expanded Relative Operator Entropies and Operator Valued α-Divergence

For strictly positive operators A and B, and for x ∈ [0,1] and r ∈[-1,1], we investigate the operator power mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 If r = O, this is reduced to the geometric operator mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 Since A #0,r B = A and A #l,r B = B, weregard A#t,rB as apath combining A and B.Our aim is to show the essential properties of St,r （AIB）. The Tsallis relative operator entropy by Yanagi, Kuriyama and Furuichi can also be expanded, and by using this, we can give an expanded operator valued a-divergence and obtain its properties.

Basic Entropies for Positive-Definite Matrices

We extend basic entropies in the classical information theory to matrix ones in the quantum information theory. Then we show that relations between matrix entropies similar to the classical ones hold.

EVALUATION OF TROPICAL CYCLONE GENESIS PRECURSORS WITH REI ATIVE OPER ATING CHARACTERISTICS(ROC)IN HIGH-RESOLUTION ENSEMBLE FORECASTS:HURRICANE ERNESTO

Identifying the environmental conditions that control tropical cyclone(TC)genesis is a challenging problem.This study examines a new method to evaluate the precursors of TC genesis using high-resolution ensemble forecasts and relative operating characteristic(ROC)diagrams.With an advanced research version of the Weather Research and Forecasting(WRF)model,high-resolution ensemble forecasts(at 5 km horizontal resolution)are conducted in various configurations using a bred vector method to form a set of 140 ensemble members for predicting Hurricane Ernesto’s genesis.Basic evaluation shows that high-resolution ensemble forecasts are able to predict well-developed TCs,whereas the NCEP Global Ensemble Forecast System(GEFS)fails to do so.This set of 140 ensemble members is employed to study the precursors of Hurricane Ernesto’s genesis by contrasting the genesis and nongenesis cases.Specifically,ROC curves,composite figures for genesis and nongenesis cases,and Kolmogorov-Smirnov tests are applied to characterize the relationship between important environmental parameters near the beginning of the simulation and genesis likelihood 15-18 h later.It is found that moist conditions at 850 hPa,vertical wind shear,the strength of the 850 hPa pre existing wave,and upper-level warming play notable roles in Ernesto’s genesis.

A New Observation Operator for the Assimilation of Satellite-Derived Relative Humidity:Methodology and Experiments with Three Sea Fog Cases over the Yellow Sea

Assimilation of satellite-derived relative humidity(Satellite-RH)is capable of improving sea fog forecasts by saturating the background in the observed foggy areas.Previous studies have achieved saturation by increasing the moisture only(Method-q).However,this method can lead to large wetting and warming biases within the marine atmospheric boundary layer(MABL).A new method using an RH observation operator(Method-RH)is designed to alleviate these biases by simultaneously adjusting the moisture and the temperature.For comparison,saturation is also achieved by decreasing the temperature only(Method-t).The three Satellite-RH assimilation methods are implemented within the Gridpoint Statistical Interpolation-based three-dimensional variational system and examined for three sea fog cases over the Yellow Sea.The three cases on 28 April 2007,9 April 2009,and 29 March 2015 fail to be predicted without the Satellite-RH assimilation as their MABLs have both warming and drying,drying,and warming biases,respectively.Intercomparisons and evaluations show that Method-RH has the best overall performance of the three methods in terms of the forecast of sea fog and MABL structures as only Method-RH can fully or partially address all the bias scenarios in forecasting sea fog.Compared with Method-q,Method-RH produces more well-defined sea fog areas by adding a smaller amount of moisture as well as decreasing the temperature.Compared with Methodt,Method-RH enlarges the sea fog areas by increasing the amount of moisture in addition to the cooling.

INVERSE SCATTERING PROBLEM FOR ONE-DIMENSIONAL SCHRDINGER OPERATORS RELATED TO THE GENERAL STARK EFFECT

This paper disccusses the inverse scattering problem for one-dimensional Schrodinger operatorsrelated to the general Stark effect. We provide a ganeral framework which can be applied both to theStark-effect operator and the ordinary Schrodinger operator.